Degeneration of N-solitons and interaction of higher-order solitons for the (2+1)-dimensional generalized Hirota-Satsuma-Itoequation

Abstract

Abstract In this paper, the evolutionary behavior of N-solitons for a (2+1)-dimensional generalized Hirota-Satsuma-Ito equation is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T = 1, 2, 3) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M = 1, 2, 3) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Besides, the interaction phenomenon between 1-order lump solution and N-soliton (N takes any positive integer) solution is investigated, and we give a computational proof process and an example. Meanwhile, we also provide a large number of three-dimensional and two-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.